This invention relates to a method of analysis of biological cell materials and particularly, but not exclusively, to analysis or monitoring of materials comprising enzymes in membranes, as well as analysis of substrates for such cell materials and enzymes.
The linear passive audio and radio frequency electrical properties of biological cell materials are well known. In the frequency range below about 10 MHz, these properties are conveniently measured as the equivalent parallel conductance and capacitance of an electrochemical cell containing the system under study. Up to these radio-frequencies, most biological cell materials exhibit two major dispersions, known as the alpha and beta dispersions. Whilst other sub-dispersions contribute to these major dispersions, and may occasionally be separated from them, the beta dispersion of tissues and cell suspensions is caused predominantly by the build-up of charge at the essentially non-conducting plasma membrane surfaces. The alpha dispersion, though not always dependent upon the ionic strength of the medium, is usually accounted for mainly in terms of the relaxation of counter-ions tangential to the charged surfaces of the membrane and cell envelope.
In the simplest case of dielectric relaxation, that of the reorientation of a "hard" sphere with a permanent dipole moment, the statistical mean of the cosine of the angle which the dipole makes with the field, has a field-dependence following the Langevin function: EQU cos &lt;.theta.&gt;=coth x.times.1/x,
where x=.mu.E/kT. A Taylor expansion of this series shows that substantial deviations from linearity do not occur for values of x less than approximately 1, and that to an excellent approximation cos &lt;.theta.&gt;=.mu.E/3 kT. Thus the dielectric displacement current is proportional to the magnitude of the exciting field, and their ratio, the admittance, independent of it. These properties are characteristic of a linear system obeying the fluctuation-dissipation theorem.
Due to the fact that they are suspended or dissolved in conductive aqueous media, biological dielectrics are "lossy". Thus electrochemical reactions, and especially Joule heating, restrict the AC voltages that may be applied to them, and the dielectric properties of biological cell materials are typically measured using macroscopic electrical fields E of the order 0.1-5 V.cm.sup.-1. Given the effective dipole moments usually encountered, the Langevin factor .mu.E/kT is normally minuscule, and, as judged by the independence of the measured admittance from the exciting field, well within the range of linearity.
It is known to measure the linear properties of biological materials using impedimetric instruments designed to filter out currents and voltages at frequencies other than the fundamental. This results in materials which appear to have linear characteristics but are in fact non-linear dielectrics.